James Mercer FRS

Royal Society

The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...

 (15 January 1883 – 21 February 1932) was a mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

, born in Bootle

Bootle

Bootle is a town within the Metropolitan Borough of Sefton in Merseyside, England, and a 'Post town' in the L postcode area. Formally known as Bootle-cum-Linacre, the town is 4 miles  to the north of Liverpool city centre, and has a total resident population of 77,640.Historically part of...

, close to Liverpool

Liverpool

Liverpool is a city and metropolitan borough of Merseyside, England, along the eastern side of the Mersey Estuary. It was founded as a borough in 1207 and was granted city status in 1880...

, England

England

England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...

.
He was educated at University of Manchester

University of Manchester

The University of Manchester is a public research university located in Manchester, United Kingdom. It is a "red brick" university and a member of the Russell Group of research-intensive British universities and the N8 Group...

, and then University of Cambridge

University of Cambridge

The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...

. He became a Fellow, saw active service at the Battle of Jutland

Battle of Jutland

The Battle of Jutland was a naval battle between the British Royal Navy's Grand Fleet and the Imperial German Navy's High Seas Fleet during the First World War. The battle was fought on 31 May and 1 June 1916 in the North Sea near Jutland, Denmark. It was the largest naval battle and the only...

 in World War I

World War I

World War I , which was predominantly called the World War or the Great War from its occurrence until 1939, and the First World War or World War I thereafter, was a major war centred in Europe that began on 28 July 1914 and lasted until 11 November 1918...

, and after decades of suffering ill health died in London, England.

He proved Mercer's theorem

Mercer's theorem

In mathematics, specifically functional analysis, Mercer's theorem is a representation of a symmetric positive-definite function on a square as a sum of a convergent sequence of product functions. This theorem, presented in , is one of the most notable results of the work of James Mercer...

, which states that positive definite kernels can be expressed as a dot product

Dot product

In mathematics, the dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers and returns a single number obtained by multiplying corresponding entries and then summing those products...

 in a high-dimensional space. This theorem is the basis of the kernel trick

Kernel trick

For machine learning algorithms, the kernel trick is a way of mapping observations from a general set S into an inner product space V , without ever having to compute the mapping explicitly, in the hope that the observations will gain meaningful linear structure in V...

(applied by Aizerman), which allows linear algorithms to be easily converted into non-linear algorithms.